The present invention relates to computer orientation and animation of objects in three dimensions (3D), and more particularly to a method of image orientation and animation for rotating video pictures in real time and interpolating the rotation orientation of the video pictures to animate a sequence of keyframes based upon representing the rotation orientation of an object in three dimensional space using quaternions.
Computer animation of three dimensional objects imitates the key frame techniques of traditional animation, using key positions in space instead of key drawings. The general position of a rigid body can be given by combining a translation with a rotation. Computer animators key such transformations to control both simulated cameras and objects to be transformed. The common prior solution, as apparently illustrated by the ADO Digital Video Effects (DVE) System of Ampex Corporation, Redwood City, Calif. and by the Encore Digital Video Effects System of Quantel, Inc., Salt Lake City, Utah, used three Euler anglss interpolated independently, but this did not produce an ideal solution. Representing the orientation in terms of three angles has an adverse effect on both the real time (update) mode and the interpolation (run) mode. In the update mode using Euler angles to represent the rotation orientation of the image, the operator has generally very little control over the response of the image when an attempt is made to modify one or more angles of rotation. The reason for the unpredictable behavior is due to the fact that rotations are not commutative. If, for example, an orientation is specified by three angles of rotation A, B and C about the X, Y and Z axes, respectively, in that particular order, then a modification to the angle B generally results in unexpected behavior. This is true because the orientation is constructed from the identity rotation with the new B, but in the original order A, B.sub.new, C. The image in general does not appear to have been rotated from its previous orientation about the Y-axis of the image or the Y-axis of the display surface, or monitor.
Other 3D DVE products animate between rotation orientation keyframes by independently interpolating each of the three Euler angles to produce an inbetween image. In doing so the interpolated orientations do not lie directly inbetween the two given rotation orientations. In general undesirable and indirect rotation paths are taken.
The use of quaternions in representing general rotations was first suggested in an article entitled "Animating Rotation with Quaternion Curves", SIGGRAPH '85, Vol. 19, No. 3, July 1985 by Ken Shoemake. What is suggested is an animator sitting at a workstation interactively establishing a sequence of keys for, as an example, camera orientation. The interpolating algorithm does not depend upon the nature of the interface the animator sees--all needed information is contained in the sequence of keys. The orientations are represented as matrices, so a conversion step follows. The matrices are converted to a sequence of neighboring quaternions, q.sub.n, on a unit four-dimensional sphere. Each quaternion within the sequence becomes the end point of two spherical Bezier curves. Between each quaternion pair, q.sub.n and q.sub.n+1, two additional points, a.sub.n and b.sub.n+1, are added to control motion through joints. At this point time becomes a parameter along the composite curve. As the frame number increases, the parameter enters and leaves successive curve pieces. Within each piece a local version of the parameter, u, is adjusted to run from 0 to 1. The Bezier geometric construction produces an interpolated quaternion, q.sub.n+u, from q.sub.n, a.sub.n, b.sub.n+1, q.sub.n+1 and u. The new interpolated quaternion is converted into a matrix which is used in rotating a list of object vectors for transforming.
Another suggestion for interpolating between keyframes was suggested by Doris H. U. Kochanek and Richard H. Bartels in a paper entitled "Interpolating Splines with Local Tension, Continuity, and Bias Control" published in Computer Graphics, Vol. 18, No. 3, July 1984. This method uses Hermite interpolation basis functions as the cubic interpolation polynomial having three control parameters: tension, continuity and bias. These control parameters are used to adjust the first derivatives of adjoining polynomial segments to produce desired results.
What is desired is an orientation and animation technique for rotation of video pictures which provide smooth, predictable, natural motion in real time in response to updated orientations and smooth, essentially direct path interpolation between key frames during animation runs by defining rotation about any axis in three dimensions with respect to either the video picture itself or the display surface.